Engineering Board Exam Reviewer · Circular and Cyclic Permutations · medium

In how many ways can 5 men and 5 women be seated around a round table so that men and women alternate?

  1. 2,880
  2. 14,400
  3. 5,760
  4. 720

Answer

A. 2,880

Solution

Seat the 5 men around the table first: (5-1)!=24 ways. The 5 women then occupy the 5 gaps between them in 5!=120 ways. Total =24×120=2,880.

More Circular and Cyclic Permutations questions

  1. In how many ways can 8 people be seated around a circular table?
  2. In how many ways can 6 people be seated at a round table?
  3. In how many ways can 5 different keys be arranged on a key ring? (A key ring can be flipped over, so clockwise and counterclockwise…
  4. In how many ways can 4 couples (8 people) be seated at a round table if each couple must sit together?
  5. In how many ways can 7 people be seated at a round table if two specific people must sit next to each other?
  6. In how many ways can 5 married couples be seated around a round table if each husband must sit next to his wife?
  7. In how many ways can 4 Americans and 3 Filipinos be seated around a circular table if all the Filipinos must sit together?
  8. In how many ways can 6 people be seated around a round table if two particular people refuse to sit next to each other?
  9. In how many ways can 7 different beads be strung on a necklace (the necklace can be turned over)?

All Circular and Cyclic Permutations questions